Question: $B$ is the midpoint of $\overline{AC}$ $A$ $B$ $C$ If: $ AB = 2x + 1$ and $ BC = 5x - 14$ Find $AC$.
Solution: A midpoint divides a segment into two segments with equal lengths. ${AB} = {BC}$ Substitute in the expressions that were given for each length: $ {2x + 1} = {5x - 14}$ Solve for $x$ $ -3x = -15$ $ x = 5$ Substitute $5$ for $x$ in the expressions that were given for $AB$ and $BC$ $ AB = 2({5}) + 1$ $ BC = 5({5}) - 14$ $ AB = 10 + 1$ $ BC = 25 - 14$ $ AB = 11$ $ BC = 11$ To find the length $AC$ , add the lengths ${AB}$ and ${BC}$ $ AC = {AB} + {BC}$ $ AC = {11} + {11}$ $ AC = 22$